This invention relates to an abrasive device and an abrasive method for abrading a curved or an aspheric surface, which has no axis of rotative symmetry, of optical elements such as aspheric optical lenses or mirrors or of die assembly such as an injection molding die for producing the optical elements. More specifically, this invention relates to a cost-effective abrasive device and abrasive method having high processing precision.
Japanese unexamined patent publication 5-57606 (referred to as JP-A) discloses a prior abrasive device for abrading curved surface or aspheric surface, which has no axis of rotative symmetry, of optical elements such as aspheric optical lenses or mirrors or of die assembly such as injection molding die for producing the optical elements.
FIG. 14 shows the prior abrasive device. The abrasive device comprises a level block 2, a horizontal movement stage 1A for moving the workpiece 3 in a horizontal direction, a configuration measuring element 1B for measuring the surface configuration of a work surface 3A of the workpiece 3 being transported by the horizontal movement stage 1A and an abrading processor 1C for abrading the work surface 3A of the workpiece 3 being transported by the horizontal movement stage 1A according to a surface configuration data acquired through the configuration measuring element 1B.
The horizontal movement stage 1A comprises a Y-axis table 4 slidably mounted on the level block 2, a ball screw 5 being gear-engaged with an internal nut (not shown) of the Y-axis table, a motor 6 for moving the Y-axis table along to the Y-axis direction by rotating the ball screw 5, X-axis table 7 mounted slidably on the Y-axis table 4, a ball screw 8 being gear-engaged with an internal nut (not shown) of the X-axis table, a motor 9 for moving the X-axis table 7 along to the X-axis direction by rotating the ball screw 8 and a .theta. table 10 rotatably mounted by an internal motor (not shown).
The abrading processor 1C comprises L-shaped abrading frames 11A, 11B and 11C mounted on the level block 2, Z-direction tilting device 13 mounted on one end of each abrading frame 11A, 11B and 11C through a mounting plate 12 and an abrading head 14 mounted on the Z-direction tilting device.
FIG. 15 shows a configuration of the Z-direction tilting device 13. The Z-direction tilting device 13 comprises a triangular mounting plate 15 having three apexes 15a, each of which is fixed on the mounting plate 12, shafts 16A, 16B and 16C (not shown) each of which is mounted on one surface of the triangular mounting plate in parallel to one of three facets of the triangular mounting plate respectively, blocks 17A, 17B and 17C each of which is mounted rotatably around one of shafts 16A, 16B and 16C respectively, abrading arms 18A, 18B and 18C each of which defines an opening for incorporating one of those blocks 17A, 17B and 17C so that each block is slidably engaged perpendicularly to inner facets of each abrading arm, ball screws 19A, 19B and 19C being gear-engaged with each inner nut (not shown) of each block 17A, 17B and 17C and mounted in each opening of on abrading arm 18A, 18B and 18C, motors 20A, 20B and 20C for moving each abrading arm 18A, 18B and 18C in vertical direction by rotating each ball screw 19A, 19B and 19C and triangular mounting plate 22 for mounting an abrading head thereon, which is mounted on abrading arms 18A, 18B and 18C through universal joints 21A, 21B and 21C.
FIG. 16 shows a configuration of the abrading head 14. The abrading head 14 comprises a cylindrical abrading tip 23 for abrading the work surface 3A of the workpiece 3, an abrading tip holder 24 for holding the abrading tip 23, a pressure applying device 26 for applying a constant pressing force to the abrading tip 23 through a loading shaft 25 and a rocking device 27 for rocking, i.e., reciprocating, the abrading tip 23 in an arrow direction D.
The constant pressure applying device 26 comprises a voice coil motor (not shown), plate spring (not shown) and loading sensor (not shown) each of which are attached to the loading shaft 25 for always maintaining an adjusted pressing force. The loading shaft 25 also comprises a displacement sensor (not shown) for detecting an updated amount of displacement of the loading shaft 25 in the direction of its axis.
The rocking device 27 comprises a crank 29 mechanically engaged to a rotating shaft 28A of the motor 28, a connecting rod 30 for transforming the rotating movement of the crank 29 into a reciprocal movement and a slider 32 that is fixed on a casing of the constant pressure applying device 26 and slidably mounted on a slide shaft 31 imposed by the reciprocal movement.
In a practical abrading process utilizing this device, primarily, abrasive is applied onto the work surface 3A of the workpiece 3, and the abrading tip 23 is placed onto the work surface 3A by moving the abrading head 23 downward by actuating the Z-direction tilting device 14. Then, the abrading tip 23 is reciprocally moved in the arrow direction D by actuating the rocking device 27 while a certain pressing force is applied onto the abrading tip 23 by the constant pressure applying device 26 in order to abrade the work surface 3A of the workpiece 3 with the abrading tip 23. At this time, the abrading head 14 scans and abrades the working surface 3A synchronously controlled by respective movements of Y-axis table 4, X-axis table 7, .theta. table 10 and Z-direction tilting device 14 based on a scanning pattern and a scanning speed distribution, discussed below, in accordance with the detected surface configuration of the work surface 3A so that the pressing direction of the abrading tip 23 is always consistent with the direction of a normal line on the work surface 3A and so that the amount of the displacement of the loading shaft 25 acquired by the displacement sensor is always constant. Since the abraded amount is in proportion to each of the pressing force, relative moving speed with the workpiece and dwell time of the abrading tip 23, a dwell time distribution of the abrading tip 23, i.e., scanning speed distribution of the abrading tip 23, required to produce an approximate objective configuration on the work surface 3A is estimated from both a hypothetical unit amount to be abraded of the work surface 3A by the abrading tip 23 per unit time when the pressing force on the abrading tip 23 and the relative moving speed with the work surface 3A is maintained constant and a difference between practically measured configuration of the work surface 3A measured by the configuration measuring element 1B and the objective surface configuration thereof.
The aforementioned prior abrasive device has the following disadvantages:
(1) Since the abrading tip has cylindrical shape and the contact area with the work surface is relatively large, a pressing force distribution of the abrading tip is easily changed even while the pressing force thereof is maintained constant when a curvature of the work surface where the abrading tip contacts is changed in accordance with the scanning movement of the abrading head. Furthermore, the relative speed distribution or pressing force distribution of the abrading tip is easily changed while the contacting location of the abrading tip on the work surface moves because the direction of the normal line on the work surface is varied according to the scanning of the abrading tip in an area where the radius of curvature of the work surface is relatively small. Thus, the unit amount of the work surface to be abraded by the abrading tip per unit time, i.e., equal to the product of the pressing force, the relative moving speed and the dwell time of the abrading tip, is easily changed according to the variety of surface configuration of the work surface to reduce the processing precision. PA1 (2) Since the relative scan of the abrading head is performed and controlled by six controlling axes, i.e., six controlling shafts, the design of the abrasive device tend to be complicated to increase manufacturing costs. PA1 (3) Since the abrading head is scanned in response to the detected configuration of the work surface, huge amounts of controlling data are required to control the abrading head even in a relatively short scanning distance, thus, calculating time of a controller increases to reduce the scanning speed of the abrading head. Therefore, the processing precision decreases since the total amount of work surface to be abraded is difficult to be controlled by the mere control of the scanning speed of the abrading head. PA1 (4) Since the scanning of the abrading head is controlled by a synchronous control of respective driving shafts for abrading the entire work surface, the controlling data tend to be huge and thus, the manufacturing cost of the abrading device tends to increase according to increases in memory capacity of the controller.
In addition, in this prior abrasive device, since the position of the abrading head is varied based on a standard position different from the contacting point between the work surface and the abrading tip, the horizontal position and vertical position of the abrading tip are also changed according to the position change of the abrading head, therefore, horizontal position or vertical position of the abrading head or workpiece itself has to also be compensated accordingly. Furthermore, since such compensation on the positioning data will be a high load when the variation of normal lines on the work surface is huge, the scanning speed of the abrading tip can not compete with the commanded scanning speed because of the mechanical limitation on scanning speed or the calculation speed of the processor. Thus, the dwell time distribution of the abrading head is far from the commanded dwell time distribution which decreases the processing precision.